CTL 免疫反应和时滞分布下 CD4+T 细胞和巨噬细胞中 HIV 感染的全局稳定性。
Global stability of HIV infection of CD4+ T cells and macrophages with CTL immune response and distributed delays.
机构信息
Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia ; Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut 71511, Egypt.
Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia.
出版信息
Comput Math Methods Med. 2013;2013:653204. doi: 10.1155/2013/653204. Epub 2013 Dec 2.
We study the global stability of a human immunodeficiency virus (HIV) infection model with Cytotoxic T Lymphocytes (CTL) immune response. The model describes the interaction of the HIV with two classes of target cells, CD4(+) T cells and macrophages. Two types of distributed time delays are incorporated into the model to describe the time needed for infection of target cell and virus replication. Using the method of Lyapunov functional, we have established that the global stability of the model is determined by two threshold numbers, the basic reproduction number R0 and the immune response reproduction number R0(∗). We have proven that, if R0 ≤ 1, then the uninfected steady state is globally asymptotically stable (GAS), if R0* ≤ 1 < R0, then the infected steady state without CTL immune response is GAS, and, if R0* > 1, then the infected steady state with CTL immune response is GAS.
我们研究了具有细胞毒性 T 淋巴细胞（CTL）免疫反应的人类免疫缺陷病毒（HIV）感染模型的全局稳定性。该模型描述了 HIV 与两类靶细胞（CD4(+)T 细胞和巨噬细胞）的相互作用。模型中引入了两种分布时滞，以描述感染靶细胞和病毒复制所需的时间。利用李雅普诺夫泛函方法，我们已经确定模型的全局稳定性由两个阈值数决定，基本繁殖数 R0 和免疫反应繁殖数 R0(∗)。我们已经证明，如果 R0 ≤ 1，则未感染的稳定状态是全局渐近稳定的（GAS），如果 R0* ≤ 1 < R0，则没有 CTL 免疫反应的感染稳定状态是 GAS，并且，如果 R0* > 1，则具有 CTL 免疫反应的感染稳定状态是 GAS。
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